Linear systems with Markov jumps and multiplicative noises: the constrained total variance problem.

• Ano de defesa: 2016
• Autor(a) principal: Barbieri, Fabio
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Controle estocástico; Controle ótimo; Investimentos (Otimização); Linear systems; Maximum variance; Optimal control; Portfolio optimization; Sistemas lineares; Stochastic control; Variância máxima
• Link de acesso: http://www.teses.usp.br/teses/disponiveis/3/3139/tde-17032017-100317/

In this work we study the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and multiplicative noises. We consider the multiperiod and finite time horizon optimization of a mean-variance cost function under a new criterion. In this new problem, we apply a constraint on the total output variance weighted by its risk parameter while maximizing the expected output. The optimal control law is obtained from a set of interconnected Riccati difference equations, extending previous results in the literature. The application of our results is exemplified by numerical simulations of a portfolio of stocks and a risk-free asset.